Since this cash flow will remain the same forever, the present value of cash flows available tothe firm’s equity holders is a perpetuity. We can discount at the levered cost of equity, so, thevalue of the company’s equity is:PV(Flow-to-equity) = $194,220/.19PV(Flow-to-equity) = $1,022,210.53b.The value of a firm is equal to the sum of the market values of its debt and equity, or:VL=B+SWe calculated the value of the company’s equity in parta, so now we need to calculate thevalue of debt. The company has a debt-to-equity ratio of .40, which can be written algebraicallyas:B/S= .40We can substitute the value of equity and solve for the value of debt, doing so, we find:B/$1,022,210.53 = .40B= $408,884.21So, the value of the company is:V= $1,022,210.53 + 408,884.21V= $1,431,094.744.a.In order to determine the cost of the firm’s debt, we need to find the yield to maturity on itscurrent bonds. With semiannual coupon payments, the yield to maturity of the company’s bondsis:$1,080 = $32.50(PVIFAR%,30) + $1,000(PVIFR%,30)R= .028497, or 2.8497%401

402 – SOLUTIONS MANUALSince the coupon payments are semiannual, the YTM on the bonds is:YTM = 2.8497% × 2YTM = 5.70%b.We can use the Capital Asset Pricing Model to find the return on unlevered equity. According tothe Capital Asset Pricing Model:R0=RF+ βUnlevered(RM–RF)R0= .035 + .95(.11 – .035)R0= .1063, or 10.63%Now we can find the cost of levered equity. According to Modigliani-Miller Proposition II withcorporate taxes:RS=R0+ (B/S)(R0–RB)(1 –TC)RS= .1063 + (.40)(.1063 – .0570)(1 – .21)RS= .1218, or 12.18%c.In a world with corporate taxes, a firm’s weighted average cost of capital is equal to:RWACC= [B/(B+S)](1 –TC)RB+ [S/(B+S)]RSThe problem does not provide either the debt-value ratio or equity-value ratio. However, thefirm’s debt-equity ratio is:B/S= .40Solving forB:B= .4SSubstituting this in the debt-value ratio, we get:B/V= .4S/(.4S+S)B/V= .4/1.4B/V= .29And the equity-value ratio is one minus the debt-value ratio, or:S/V= 1 – .29S/V= .71So, the WACC for the company is:RWACC= .29(1 – .21)(.0570) + .71(.1218)RWACC= .0999, or 9.99%

CHAPTER 18 -5.a.The equity beta of a firm financed entirely by equity is equal to its unlevered beta. Since eachfirm has an unlevered beta of 1.05, we can find the equity beta for each. Doing so, we find:North PoleβEquity= [1 + (1 –TC)(B/S)]βUnleveredβEquity= [1 + (1 – .21)($2,400,000/$4,100,000](1.05)βEquity= 1.54South PoleβEquity= [1 + (1 –TC)(B/S)]βUnleveredβEquity= [1 + (1 – .21)($4,100,000/$2,400,000](1.05)βEquity= 2.47b.We can use the Capital Asset Pricing Model to find the required return on each firm’s equity.Doing so, we find:North Pole:RS=RF+ βEquity(RM–RF)RS= .0320 + 1.54(.1090 – .0320)RS= .1502, or 15.02%South Pole:RS=RF+ βEquity(RM–RF)RS= .0320 + 2.47(.1090 – .0320)RS= .2220, or 22.20%6.a.If flotation costs are not taken into account, the net present value of a loan equals:NPVLoan= Gross Proceeds – Aftertax present value of interest and principal paymentsNPVLoan= $4,600,000 – .063($4,600,000)(1 – .21)PVIFA6.3%,10– $4,600,000/1.06310NPVLoan= $441,621.98b.The flotation costs of the loan will be:Flotation costs = $4,600,000(.025)Flotation costs = $115,000So, the annual flotation expense will be:Annual flotation expense = $115,000/10Annual flotation expense = $11,500403

404 – SOLUTIONS MANUALIf flotation costs are taken into account, the net present value of a loan equals:NPVLoan

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Term

Spring

Professor

PF Hsieh

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